CN109063757A - It is diagonally indicated based on block and the multifarious multiple view Subspace clustering method of view - Google Patents
It is diagonally indicated based on block and the multifarious multiple view Subspace clustering method of view Download PDFInfo
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Abstract
The invention proposes one kind diagonally to be indicated and the multifarious multiple view Subspace clustering method of view based on block, mainly solves the problems, such as to cluster accuracy rate present in multiple view clustering method low, realization step are as follows: obtain the multiple view data matrix of raw data set；Construct the objective function based on the multifarious multiple view subspace clustering of block diagonal sum view；Objective function is optimized；Variable in objective function after optimization is initialized；Alternating iteration is carried out to the variable in the objective function after optimization；Variable multiple view in objective function after calculation optimization indicates the value of coefficient matrix certainly；Raw data set is clustered.View diversity bound term is diagonally indicated that bound term combines with block by the present invention, more complete and accurate multiple view data set the similarity matrix of block diagonal arrangement is obtained, the accuracy rate of multiple view cluster is effectively increased, can be used for image segmentation, abnormality detection, the fields such as business analysis.
Description
Technical field
The invention belongs to computer visions and mode identification technology, are related to a kind of multiple view Subspace clustering method,
More particularly to one kind based on block diagonally indicates with the multifarious multiple view Subspace clustering method of view, can be used for image segmentation,
Abnormality detection, business statistics etc..
Background technique
With the fast development of computer information technology, data rapid growth extracts useful information in mass data
It is the significant challenge that current era is faced with knowledge, and data mining is to can be used for finding hiding information in data, mention
A kind of method of knowledge of the access in.Cluster is a kind of basic data digging method, and cluster is the side with unsupervised learning
All samples that one data is concentrated are divided into the process of multiple clusters by formula, so that the Sample Similarity in each cluster is high, different clusters
In sample similarity it is low.
Data set is indicated with single characteristic, referred to as single-view data set, is based on this kind of data set, out
It is substantially square some traditional clustering methods, such as K mean cluster, spectral clustering, density clustering and hierarchical clustering etc. have been showed
Method.But the information of raw data set included in single-view data set and imperfect.And with the development of information technology, more
Come more data sets a variety of different types of character representations, i.e. multiple view data set, traditional clustering method is utilized
The method for handling a kind of simplicity of this kind of data set is fusion early period, i.e., is coupled the multiple view data matrix of multiple view data set
Get up one data matrix of composition, recycles traditional clustering method to be clustered, but such method ignores each view
Statistical property the fact that having differences, and multiple view data matrix is tied and destroys number in multiple view data set
According to internal structure so that cluster accuracy rate it is unsatisfactory.Therefore there is the multiple view clustering method merged based on the later period, this
Class method is usually the low-dimensional insertion for clustering to each view, or obtaining multiple view data set, and then is obtained more
The consistent cluster result of viewdata collection.
The Basic practice of multiple view clustering method based on later period fusion is by the similitude and otherness consideration between view
It mainly include that the multiple view cluster based on Non-negative Matrix Factorization and the multiple view based on sub-space learning are poly- in objective function
Class.Multiple view cluster based on Non-negative Matrix Factorization usually decomposes multiple view data matrix, obtains and each view pair
The basic matrix and coefficient matrix corresponding with each view answered, are merged to obtain one to the coefficient matrix of obtained each view
The multiple view coefficient matrix of cause, and then K mean cluster is carried out to the consistent multiple view coefficient matrix of acquisition, obtain multiple view number
According to the consistent cluster result of collection.Multiple view cluster based on sub-space learning is that each sample based on multiple view data set can
To carry out linear combination with other samples in the cluster where itself, this is theoretical, and then obtains the similarity of multiple view data set
Matrix.In recent years, multiple view subspace clustering is developed on the basis of single-view Subspace clustering method, commonly
Single-view Subspace clustering method includes sparse subspace clustering and low-rank representation subspace clustering, but both single-views are sub
Spatial clustering method is to carry out on the basis of multiple subspaces in space where data set are independent from each other, and then can obtain
Coefficient matrix is indicated certainly to a data set with block diagonal arrangement, but actual data set is due to noise and abnormal data
Interference, data set is from indicating that coefficient matrix is frequently not that block is diagonal, to solve this problem, Canyi Lu, Jiashi
IEEE Transactions on of Feng, Zhouchen Liu, the Tao Mei and Shuicheng Yan in 2018
On Pattern Analysis and Machine Intelligence, entitled " Subspace Clustering by has been delivered
The article of Block Diagonal Representation ", disclosing a kind of diagonally indicates by block to carry out subspace clustering
Method, this method directly carry out block to the similarity matrix obtained from expression coefficient matrix by data set and diagonally constrain, make
The similarity matrix of its raw data set, energy are more nearly by the similarity matrix of data set obtained from expression coefficient matrix
Enough to exclude influence of the noise to initial data clustering accuracy rate to a certain extent, therefore, this method effectively increases haplopia
Scheme the accuracy rate of cluster.Up to the present, the method for the subspace clustering diagonally indicated based on block is only used for haplopia diagram data
The cluster of collection.
The existing multiple view clustering method based on sub-space learning is on the basis of above-mentioned single-view subspace clustering
It developing, by considering the consensus information between different views, diversity information in objective function, effectively increasing
There are some multiple view clustering methods based on sub-space learning, for example, Xiaochun in recent years in the accuracy rate of cluster
The IEEE conference on of Cao, Changqing Zhang, Huazhu Fu and Si Liu et al. people in 2015
On Computer Vision and Pattern Recognition, entitled " Diversity-induced Multi- has been delivered
The article of view Subspace Clustering " discloses the multiple view Subspace clustering method of species diversity induction, is
The multifarious information of multiple view data set is made full use of, this method utilizes Hilbert-Schmidt's independence criterion
The diversity information for obtaining original multiple view data set, effectively increases the cluster accuracy rate of multiple view data set, and this method is false
If multiple view data set multiple subspaces in space be independent from each other, i.e., multiple view data matrix from indicating coefficient
Matrix is that block is diagonal, but the multiple view data set in reality, due to being influenced by noise, multiple view indicates coefficient square certainly
Battle array is frequently not that block is diagonal, and this method does not account for this problem, and then affects multiple view cluster data result
Accuracy rate.
Summary of the invention
It is an object of the invention to overcome above-mentioned the shortcomings of the prior art, propose it is a kind of based on block diagonally indicates with
The multifarious multiple view Subspace clustering method of view, for improving the accuracy rate of multiple view cluster data.
Technical thought of the invention is: obtaining the multiple view data matrix of raw data set, each viewing matrix is decomposed
For viewing matrix itself, corresponding view indicates that coefficient matrix, the view of multiple views indicate coefficient matrix structure certainly certainly with the view
Coefficient matrix is indicated certainly at multiple view, and utilizes the reconstructed error item of multiple view data matrix decomposition, view diversity bound term
With the diagonal bound term of block of multiple view incidence matrix, building is diagonally indicated based on block and the multifarious multiple view subspace of view is poly-
The objective function of class indicates that coefficient matrix constructs the phase of raw data set by the multiple view obtained after optimization object function certainly
Like degree matrix, the cluster result of raw data set is obtained using spectral clustering.Realize that steps are as follows:
(1) the multiple view data matrix of raw data set is obtained
Extract different types of characteristic, same characteristic features data group respectively from the multiple image that raw data set includes
At viewing matrix, the multiple view data matrix of multiple viewing matrix composition raw data setsWherein, X(v)Indicate v
A viewing matrix, v=1,2 ..., m, m indicate the number of viewing matrix, m >=2；
(2) building is diagonally indicated based on block and the objective function O of the multifarious multiple view subspace clustering of view, realization walk
Suddenly are as follows:
(2a) willIt is decomposed intoCoefficient matrix is indicated certainly with multiple viewIt willWithWithThe difference of product reconstructs item as errorAnd it calculates's
MeasurementWherein, Z(v)Indicate v-th of viewing matrix X(v)From indicate coefficient matrix,It indicates
Square of matrix F norm；
(2b) utilizes Hilbert-Schmidt's independence criterion, constructs view diversity bound termAnd it setsWeight be λ1, wherein
I indicates that unit matrix, N indicate the number at raw data set sample number strong point, and 1 expression element is all 1 N-dimensional vector, tr ()
The mark of representing matrix, ()TThe transposition of representing matrix；
(2c) calculates multiple view incidence matrixWherein, | | table
Show the matrix formed after taking absolute value to each element of matrix, W(v)Indicate v-th of viewing matrix X(v)Incidence matrix；
(2d) is calculatedLaplacian MatrixConstructionBlock diagonally indicate bound termW(v)Block diagonally indicate bound termFor
And it setsWeight be λ2, wherein Diag () indicates the diagonalization of vector, and K indicates that initial data concentrates sample
The number of the classification of data point, 2≤K < N, λi(Y) it indicates the characteristic value in the set G of the characteristic value of matrix Y according to from small
The ith feature value of the set G' of the characteristic value obtained after being arranged to big sequence, i=1,2 ..., K；
(2e) willIt is weighted addition, is obtained
It is diagonally indicated based on block and the objective function O of the multifarious multiple view subspace clustering of view:
(3) objective function O is optimized:
By the way that the block weighted in objective function O is diagonally indicated bound termIt replaces withObjective function O' after being optimized:
Wherein,It indicatesSubstitution matrix variables, J(v)Indicate Z(v)Substitution matrix variables,It indicatesWithError term,It indicatesMeasurement, λ3
It indicatesWeight,It indicatesCompanion matrix variable, U(v)It indicates
Companion matrix variable, U(v)Be constrained to C, C is indicatedAnd tr (U(v))=K,Indicate that B-A is positive semidefinite
Matrix,<, the inner product of>representing matrix,
(4) variable in the objective function O' after optimization is initialized:
By the variable in O'WithIn include all elements be initialized as
0；
(5) alternating iteration is carried out to the variable in the objective function O' after optimization:
To the variable in O'WithAlternating iteration is carried out, is obtained and each change
Measure corresponding iteration more new-standard cementWith
(6) variable in the objective function O' after calculation optimizationValue:
The maximum number of iterations of (6a) setting O'；
(6b) utilizes the iteration more new-standard cement of each variable in O'WithIt is right
Variable in O'WithIt is iterated update, obtains updated multiple view certainly
Indicate coefficient matrix
(7) raw data set is clustered:
The similarity matrix S of (7a) calculating raw data set；
The cluster result of (7b) calculating raw data set:
(7b1) carries out diagonalization to the vector t that every a line of similarity matrix S is summed, and obtains the degree matrix D of S, and
The Laplacian Matrix L of S is calculated,
(7b2) carries out Eigenvalues Decomposition to Laplacian Matrix L, obtains each characteristic value pair in characteristic value collection E and E
The matrix T for the feature vector composition answered；
(7b3) arranges the characteristic value in E according to sequence from small to large, obtains characteristic value collection E', takes E''s
Preceding K eigenvalue cluster is at set EK, and selection and E from TKIn the corresponding feature vector composition characteristic vector of each characteristic value
Matrix T', then using the normalized result of the every a line of T' as sample number strong point；
(7b4) randomly selects K sample number strong point in T', and using each sample number strong point as the poly- of initial one kind
Class center obtains the cluster centre set R of K classification；
(7b5) calculates the Euclidean distance of each cluster centre of each sample number strong point into R in T', and by each sample number
Strong point is assigned to classification belonging to the smallest cluster centre of itself Euclidean distance, calculates the sample number for belonging to k-th of classification
Cluster centre of the mean value at strong point as k-th of classification, obtains the cluster centre of K classification, and realization is updated R, wherein
K=1,2 ..., K；
(7b6) repeats step (7b5), until cluster centre set R is no longer changed, obtains initial data
The cluster result of collection.
Compared with prior art, the present invention having the advantage that
The present invention is decomposed into multiple view data matrix and multiple view certainly when constructing objective function, by multiple view data matrix
It indicates coefficient matrix, constructs view diversity bound term using Hilbert-Schmidt's independence criterion, take full advantage of
The diversity information of multiple view, and diagonally indicate that bound term makes multiple view incidence matrix by the block of construction multiple view incidence matrix
It is that block is diagonal, by the way that view diversity bound term and block are diagonally indicated that bound term combines the phase so that raw data set
There is more complete block diagonal arrangement, therefore the similarity moment of available more accurate raw data set like degree matrix
Battle array, compared with prior art, effectively increases the accuracy rate of multiple view cluster data.
Detailed description of the invention
Fig. 1 is implementation flow chart of the invention；
Fig. 2-Fig. 3 is the multiple view Subspace clustering method of the invention induced with existing diversity in MSRC-v1 data
Cluster accuracy rate simulation result comparison diagram under collection and the hand-written volumetric data set of UCI；
Specific embodiment
In the following with reference to the drawings and specific embodiments, present invention is further described in detail.
Referring to Fig.1, based on block diagonally indicates with the multifarious multiple view Subspace clustering method of view, including walk as follows
It is rapid:
The multiple view data matrix of step 1) acquisition raw data set
Since initial data is concentrated in each image for including comprising a plurality of types of features, include from raw data set
Different types of characteristic is extracted in multiple image respectively, same characteristic features data form viewing matrix, multiple viewing matrix groups
At the multiple view data matrix of raw data setWherein, X(v)Indicate v-th of viewing matrix, v=1,2 ..., m, m table
Show the number of viewing matrix, m >=2.
Step 2) building is diagonally indicated based on block and the objective function O of the multifarious multiple view subspace clustering of view, real
Existing step are as follows:
(2a) initial data concentrates the similarity between sample in order to obtain, willIt is decomposed intoWith more views
Figure indicates coefficient matrix certainlyIn order to obtain useWithIt indicatesInconsistency, willWithWithThe difference of product reconstructs item as errorIn order to measure useWithIt indicatesInconsistency size, calculateMeasurementWherein, Z(v)Indicate v-th of viewing matrix X(v)From indicate coefficient matrix,Representing matrix F
Square of norm；
(2b) is applied for the information for adequately each view of multiple view data set being utilized to be included using Hilbert-
Close spy's independence criterion, constructs view diversity bound termAnd it setsPower
Weight is λ1, whereinI indicates that unit matrix, N indicate raw data set sample
The number of notebook data point, 1 expression element are all 1 N-dimensional vector, the mark of tr () representing matrix, ()TRepresenting matrix turns
It sets；
(2c) calculates multiple view incidence matrixWherein, | | table
Show the matrix formed after taking absolute value to each element of matrix, W(v)Indicate v-th of viewing matrix X(v)Incidence matrix；
(2d) is in order to make multiple view incidence matrixStructure be that block is diagonal, calculateLaplce
MatrixConstructionBlock diagonally indicate bound termW(v)Block diagonally indicate bound termForAnd it setsWeight be λ2,
Wherein, Diag () indicates the diagonalization of vector, and K indicates that initial data concentrates the number of the classification of sample data point, 2≤K <
N, λi(Y) it indicates to obtain after being arranged the characteristic value in the set G of the characteristic value of matrix Y according to sequence from small to large
Characteristic value set G' ith feature value, i=1,2 ..., K；
(2e) is by view diversity bound termIt is diagonally indicated with multiple view from expression coefficient matrix block
Bound termCombine, can make the similarity matrix of raw data set that there is more complete block diagonally to tie
Structure, willIt is weighted addition, is obtained based on block pair
Angle indicates and the objective function O of the multifarious multiple view subspace clustering of view:
Step 3) optimizes objective function O:
Due in objective function O aboutSubproblem be not convex function, therefore can not obtainThe overall situation
Optimal solution, for make in objective function O aboutSubproblem be convex function, willAsSubstitution square
Battle array variable, J(v)Indicate Z(v)Substitution matrix variables, and J is set(v)Be constrained to J(v)=Z(v), calculateAsWithError termMeasurement, setting's
Weight is λ3, at this point,Due to corresponding in objective function OSubproblem
Solution is unable to get, and is utilizedAsCompanion matrix variable, and U(v)It indicatesCompanion matrix
U is arranged in variable(v)Be constrained to C, C is indicatedAnd tr (U(v))=K, the objective function O' after being optimized:
Wherein,Indicate that B-A is positive semidefinite matrix,<, the inner product of>representing matrix.
Step 4) initializes the variable in the objective function O' after optimization:
By the variable in O'WithIn include all elements initialization
It is 0, carrying out initialization to the variable in O' is the iteration operation in order to guarantee optimization algorithm.
Step 5) carries out alternating iteration to the variable in the objective function O' after optimization:
To the variable in O'WithAlternating iteration is carried out, is obtained and each change
Measure corresponding iteration more new-standard cementWithRealize step are as follows:
(I) it utilizesIteration updates multiple view indicates coefficient matrix certainlyWherein Lyap () indicates Sylvester non trivial solution；
(II) it utilizesIteration updates multiple view incidence matrixWherein, | | expression pair
The matrix that each element of matrix forms after taking absolute value；
(III) W is calculated(v)Laplacian Matrix L(v), L(v)=Diag (W(v)1)-W(v), to L(v)Eigenvalues Decomposition is carried out,
Obtain L(v)Characteristic value set E(v)And E(v)In the corresponding L of each characteristic value(v)Feature vector composition feature vector
Matrix M(v), to E(v)In element arranged to obtain the set of characteristic value according to sequence from small to largeIt takesPreceding K
M corresponding to a element(v)In feature vector composition characteristic vector matrix V(v), utilize V(v)V(v)TIteration updates W(v)Auxiliary
Matrix variables U(v), utilize V(v)V(v)TSetIteration, which updates block, diagonally indicates bound termIt is auxiliary
Help matrix variables
(IV) it utilizesIteration updatesSubstitution matrix variablesWherein,(·)+Expression remains unchanged the positive element of matrix, remaining element
For matrix composed by 0, diag () indicates the diagonal element of matrix forming a vector.
Variable in objective function O' after step 6) calculation optimizationValue:
The maximum number of iterations of (6a) setting O'；
(6b) utilizes the iteration more new-standard cement of each variable in O'WithIt is right
Variable in O'WithIt is iterated update, obtains updated multiple view certainly
Indicate coefficient matrix
Step 7) clusters raw data set:
(7a) calculates the similarity matrix S of raw data set, calculation formula are as follows:
The cluster result of (7b) calculating raw data set:
(7b1) carries out diagonalization to the vector t that every a line of similarity matrix S is summed, and obtains the degree matrix D of S, and
The Laplacian Matrix L of S is calculated,
(7b2) carries out Eigenvalues Decomposition to Laplacian Matrix L, obtains each characteristic value pair in characteristic value collection E and E
The matrix T for the feature vector composition answered；
(7b3) arranges the characteristic value in E according to sequence from small to large, obtains characteristic value collection E', takes E''s
Preceding K eigenvalue cluster is at set EK, and selection and E from TKIn the corresponding feature vector composition characteristic vector of each characteristic value
Matrix T', then using the normalized result of the every a line of T' as sample number strong point；
(7b4) randomly selects K sample number strong point in T', and using each sample number strong point as the poly- of initial one kind
Class center obtains the cluster centre set R of K classification；
(7b5) calculates the Euclidean distance of each cluster centre of each sample number strong point into R in T', and by each sample number
Strong point is assigned to classification belonging to the smallest cluster centre of itself Euclidean distance, calculates the sample number for belonging to k-th of classification
Cluster centre of the mean value at strong point as k-th of classification, obtains the cluster centre of K classification, and realization is updated R, wherein
K=1,2 ..., K；
(7b6) repeats step (7b5), until cluster centre set R is no longer changed, obtains initial data
The cluster result of collection.
Below with reference to emulation experiment, technical effect of the invention is described further.
1. simulated conditions and content
Simulated conditions:
Computer configuration surroundings are Intel (R) Core (i7-7700) 3.60GHZ central processing unit, memory in emulation experiment
32G, WINDOWS7 operating system, computer simulation software use MATLAB R2016b software.
MSRC-v1 data set and the hand-written volumetric data set of UCI is respectively adopted in emulation experiment.
Emulation content:
Emulation 1
Using the present invention and existing hidden multiple view Subspace clustering method under MSRC-v1 data set, to the standard of cluster
True rate compares emulation, and result is as shown in Figure 2.
Emulation 2
Using the present invention and existing hidden multiple view Subspace clustering method in the case where UCI writes volumetric data set, to cluster
Accuracy rate compares emulation, and result is as shown in Figure 3.
2. analysis of simulation result:
Referring to Fig. 2, under MSRC-v1 data set, when the number of test sample is respectively 28,56,84,112,140,168,
When 196, the accuracy rate of the cluster result obtained using the present invention is than the accuracy rate of the cluster result obtained using the prior art
Height, when the number of test sample is 140, the present invention is minimum compared with the cluster accuracy rate that the prior art is promoted, and is 1.0%, works as survey
When the number of sample sheet is 28, the present invention is maximum compared with the accuracy rate that the prior art is promoted, and is 5.3%.It is hand-written in UCI referring to Fig. 3
Under volumetric data set, when test sample number is respectively 100,200,300,400,500,600, using obtained cluster of the invention
As a result the accuracy rate of cluster result of the accuracy rate than being obtained using the prior art is high, and is in the number of test sample
When 200, the present invention is minimum compared with the accuracy rate that the prior art is promoted, and is 4.0%.
By the simulation result of Fig. 2-Fig. 3, under different data sets, when using different number of test data, this is utilized
Invention is above the accuracy rate using the prior art to multiple view cluster data to the accuracy rate of multiple view cluster data, this
It is because the present invention indicates the difference of different views using view diversity bound term when carrying out the cluster of multiple view data set
Information, and diagonally indicate that constraint keeps the structure of the similarity matrix of raw data set more accurate using block, with the prior art
It compares, effectively increases the accuracy rate of multiple view cluster data.
Claims (3)
1. one kind is diagonally indicated based on block and the multifarious multiple view Subspace clustering method of view, which is characterized in that including such as
Lower step:
(1) the multiple view data matrix of raw data set is obtained
Extract different types of characteristic, same characteristic features data composition view respectively from the multiple image that raw data set includes
Figure matrix, the multiple view data matrix of multiple viewing matrix composition raw data setsWherein, X(v)Indicate v-th of view
Figure matrix, v=1,2 ..., m, m indicate the number of viewing matrix, m >=2；
(2) building is diagonally indicated and the objective function O of the multifarious multiple view subspace clustering of view, realization step based on block
Are as follows:
(2a) willIt is decomposed intoCoefficient matrix is indicated certainly with multiple viewIt willWith
WithThe difference of product reconstructs item as errorAnd it calculatesMeasurementWherein, Z(v)Indicate v-th of viewing matrix X(v)From indicate coefficient matrix,Representing matrix F
Square of norm；
(2b) utilizes Hilbert-Schmidt's independence criterion, constructs view diversity bound term
And it setsWeight be λ1, whereinI indicates unit square
Battle array, N indicate the number at raw data set sample number strong point, and 1 expression element is all 1 N-dimensional vector, tr () representing matrix
Mark, ()TThe transposition of representing matrix；
(2c) calculates multiple view incidence matrixWherein, | | expression pair
The matrix that each element of matrix forms after taking absolute value, W(v)Indicate v-th of viewing matrix X(v)Incidence matrix；
(2d) is calculatedLaplacian MatrixConstructionBlock diagonally indicate bound termW(v)Block diagonally indicate bound termFor
And it setsWeight be λ2, wherein Diag () indicates the diagonalization of vector, and K indicates that initial data concentrates sample
The number of the classification of data point, 2≤K < N, λi(Y) it indicates the characteristic value in the set G of the characteristic value of matrix Y according to from small
The ith feature value of the set G' of the characteristic value obtained after being arranged to big sequence, i=1,2 ..., K；
(2e) willIt is weighted addition, is based on
Block diagonally indicates and the objective function O of the multifarious multiple view subspace clustering of view:
(3) objective function O is optimized:
By the way that the block weighted in objective function O is diagonally indicated bound termIt replaces withObjective function O' after being optimized:
Wherein,It indicatesSubstitution matrix variables, J(v)Indicate Z(v)Substitution matrix variables,
It indicatesWithError term,It indicatesMeasurement, λ3It indicatesWeight,It indicatesCompanion matrix variable, U(v)It indicatesAuxiliary
Matrix variables, U(v)Be constrained to C, C is indicatedAnd tr (U(v))=K,Indicate that B-A is positive semidefinite matrix,
<, the inner product of>representing matrix,
(4) variable in the objective function O' after optimization is initialized:
By the variable in O'WithIn include all elements be initialized as 0；
(5) alternating iteration is carried out to the variable in the objective function O' after optimization:
To the variable in O'WithAlternating iteration is carried out, is obtained and each variable pair
The iteration answered more new-standard cementWith
(6) variable in the objective function O' after calculation optimizationValue:
The maximum number of iterations of (6a) setting O'；
(6b) utilizes the iteration more new-standard cement of each variable in O'WithTo in O'
VariableWithIt is iterated update, obtains updated multiple view from expression
Coefficient matrix
(7) raw data set is clustered:
The similarity matrix S of (7a) calculating raw data set；
The cluster result of (7b) calculating raw data set:
(7b1) carries out diagonalization to the vector t that every a line of similarity matrix S is summed, and obtains the degree matrix D of S, and calculate
The Laplacian Matrix L of S,
(7b2) carries out Eigenvalues Decomposition to Laplacian Matrix L, and each characteristic value obtained in characteristic value collection E and E is corresponding
The matrix T of feature vector composition；
(7b3) arranges the characteristic value in E according to sequence from small to large, obtains characteristic value collection E', takes preceding K of E'
Eigenvalue cluster is at set EK, and selection and E from TKIn the corresponding feature vector composition characteristic vector matrix of each characteristic value
T', then using the normalized result of the every a line of T' as sample number strong point；
(7b4) randomly selects K sample number strong point in T', and using each sample number strong point as in initial a kind of cluster
The heart obtains the cluster centre set R of K classification；
(7b5) calculates the Euclidean distance of each cluster centre of each sample number strong point into R in T', and by each sample data point
It is assigned to classification belonging to the smallest cluster centre of itself Euclidean distance, calculates the sample number strong point for belonging to k-th of classification
Cluster centre of the mean value as k-th of classification, obtain the cluster centre of K classification, realization is updated R, wherein k=
1,2,…,K；
(7b6) repeats step (7b5), until cluster centre set R is no longer changed, obtains raw data set
Cluster result.
2. it is according to claim 1 based on block diagonally indicates with the multifarious multiple view Subspace clustering method of view,
It is characterized in that, carrying out alternating iteration to the variable in the objective function O' after optimization described in step (5), step is realized are as follows:
(I) it utilizesIteration updates multiple view indicates coefficient matrix certainlyWherein Lyap () indicates Sylvester non trivial solution,Indicate multiple view
Data matrix,I indicates that unit matrix, N indicate the number at raw data set sample number strong point, and 1 indicates element
It is all 1 N-dimensional vector, the mark of tr () representing matrix, ()TThe transposition of representing matrix, λ1Indicate view diversity bound termWeight, λ3Indicate error termWeight, view m indicate viewing matrix number
Mesh；
(II) it utilizesIteration updates multiple view incidence matrixWherein, | | it indicates to matrix
Each element take absolute value after the matrix that forms, W(v)Indicate v-th of viewing matrix X(v)Incidence matrix,It indicatesSubstitution matrix variables；
(III) W is calculated(v)Laplacian Matrix L(v), L(v)=Diag (W(v)1)-W(v), to L(v)Eigenvalues Decomposition is carried out, is obtained
L(v)Characteristic value set E(v)And E(v)In the corresponding L of each characteristic value(v)Feature vector composition eigenvectors matrix M(v), to E(v)In element arranged to obtain the set of characteristic value according to sequence from small to largeIt takesIt is preceding K member
M corresponding to element(v)In feature vector composition characteristic vector matrix V(v), utilize V(v)V(v)TIteration updates W(v)Companion matrix
Variable U(v), utilize V(v)V(v)TSetIteration, which updates block, diagonally indicates bound termAuxiliary moment
Battle array variable
(IV) it utilizesIteration updatesSubstitution matrix variablesIts
In,(·)+Expression remains unchanged the positive element of matrix, remaining element is formed by 0
Matrix, diag () indicates the diagonal element of matrix forming a vector, λ2Indicate that block diagonally indicates bound termWeight.
3. it is according to claim 1 based on block diagonally indicates with the multifarious multiple view Subspace clustering method of view,
It is characterized in that, calculating the similarity matrix S of raw data set, calculation formula described in step (7a) are as follows:
Wherein, | | indicate the matrix formed after taking absolute value to each element of matrix, ()TThe transposition of representing matrix,Indicate that updated multiple view indicates that coefficient matrix, m indicate the number of viewing matrix certainly.
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